Implement Virtual DOM Diffing Algorithm

You will implement a core component of modern front-end frameworks: a virtual DOM diffing algorithm. This algorithm efficiently determines the minimal set of changes required to update a real DOM tree to match a new virtual DOM tree. Mastering this is crucial for understanding how frameworks like React and Vue achieve high performance in UI updates.

Problem Description

Your task is to create a JavaScript function that takes two virtual DOM trees (an old tree and a new tree) and returns a list of "patches" representing the differences. These patches will describe how to transform the old DOM into the new DOM.

A virtual DOM node will be represented as a plain JavaScript object with the following structure:

{
  type: 'tagName', // e.g., 'div', 'span', 'h1'
  props: { ... }, // attributes and properties
  children: [ ... ] // array of child nodes (other virtual DOM nodes or strings)
}

A string child represents a text node.

The function should return an array of patch objects. Each patch object describes a specific operation to be performed on the real DOM. The possible patch types are:

• REPLACE: Replace the old node with a new node.
  • { type: 'REPLACE', newNode: virtualNode }
• UPDATE: Update the properties of an existing node.
  • { type: 'UPDATE', props: { ... } } (where props contains only the changed/added/removed properties)
• REMOVE: Remove a node from its parent.
  • { type: 'REMOVE' }
• INSERT: Insert a new node at a specific position.
  • { type: 'INSERT', newNode: virtualNode, index: number }
• TEXT: Update the text content of a text node.
  • { type: 'TEXT', content: string }

Your diffing algorithm should be recursive and handle various scenarios, including:

• Node type changes (e.g., div to span).
• Attribute additions, removals, and updates.
• Children additions, removals, and reordering.
• Text node updates.

Examples

Example 1: Replacing a node

Input:
oldTree = { type: 'div', props: {}, children: [] }
newTree = { type: 'span', props: {}, children: [] }

Output:
[
  { type: 'REPLACE', newNode: { type: 'span', props: {}, children: [] } }
]

Explanation: The root node type has changed from 'div' to 'span', so we replace the entire node.

Example 2: Updating properties and children

Input:
oldTree = {
  type: 'div',
  props: { id: 'container', className: 'old-class' },
  children: [
    { type: 'span', props: { className: 'text' }, children: ['Hello'] }
  ]
}
newTree = {
  type: 'div',
  props: { id: 'container', className: 'new-class', style: { color: 'red' } },
  children: [
    { type: 'span', props: { className: 'text' }, children: ['World'] }
  ]
}

Output:
[
  { type: 'UPDATE', props: { className: 'new-class', style: { color: 'red' } } },
  { type: 'TEXT', content: 'World' }
]

Explanation:
1. The root 'div' has its 'className' updated and a 'style' property added.
2. The child 'span' node's text content is updated from 'Hello' to 'World'.

Example 3: Adding and removing children, and reordering

Input:
oldTree = {
  type: 'ul',
  props: {},
  children: [
    { type: 'li', props: {}, children: ['Item 1'] },
    { type: 'li', props: {}, children: ['Item 2'] }
  ]
}
newTree = {
  type: 'ul',
  props: {},
  children: [
    { type: 'li', props: {}, children: ['Item A'] }, // Reordered and text updated
    { type: 'li', props: {}, children: ['Item C'] }  // Added
  ]
}

Output:
[
  { type: 'TEXT', content: 'Item A' }, // Corresponds to old Item 1, now updated
  { type: 'REPLACE', newNode: { type: 'li', props: {}, children: ['Item C'] } } // Corresponds to old Item 2, now replaced with new Item C
]

Explanation:
1. The first child ('Item 1') is matched with the first child in the new tree ('Item A'). The text is updated.
2. The second child ('Item 2') from the old tree is matched with the second child in the new tree ('Item C'). However, due to the reordering and potential for optimizations, this is often treated as a replacement of the old item with the new one. A more advanced diff might recognize 'Item C' as an insertion and 'Item 2' as a removal, but for simplicity, we can consider replacing the existing element if a direct match based on index isn't ideal.
A more sophisticated approach would involve keying for efficient reordering. Without keys, we might rely on heuristics or treat unmatched elements as removals/insertions. For this challenge, assume a simple greedy approach or that a more complex diffing would handle this. A practical diff would also try to find common sub-sequences to optimize reordering. For this exercise, focus on the core diffing logic for simpler cases and consider that reordering can be complex.

Let's refine the output for Example 3 to be more explicit about operations. A real diffing algorithm would likely aim for something like this:
Output (more detailed, reflecting actual DOM operations):
[
  // Operations on the first child of 'ul'
  { type: 'TEXT', content: 'Item A' }, // Updates the text of the first 'li'
  // Operations on the second child of 'ul'
  { type: 'REPLACE', newNode: { type: 'li', props: {}, children: ['Item C'] } } // Replaces the second 'li' with the new 'Item C'
]

A truly optimal diff would recognize 'Item 2' as removed and 'Item C' as inserted, but for this problem, focusing on matching by index and performing the necessary updates/replacements is sufficient.

Constraints

• Virtual DOM nodes will have type, props, and children properties.
• props will be a plain JavaScript object.
• children will be an array of virtual DOM nodes or strings.
• The maximum depth of the virtual DOM tree will not exceed 50.
• The maximum number of nodes in a tree will not exceed 1000.
• Your diff function should aim for a time complexity of O(N*M) in the worst case, where N and M are the number of nodes in the old and new trees respectively. However, for well-structured updates (e.g., few changes), it should perform much better.

Notes

• You'll need to compare properties carefully. If a property exists in the old tree but not the new, it should be removed. If it exists in the new but not the old, it should be added. If it exists in both and has a different value, it should be updated.
• The order of children matters. When comparing children arrays, you should iterate through them and find differences. A naive approach is to compare by index.
• Consider how to handle text nodes versus element nodes.
• When a node's type changes, it's generally more efficient to replace the entire node rather than trying to update it.
• This challenge focuses on the diffing logic. You do not need to implement the "patching" part (applying these patches to a real DOM).